Two views, one camera: mirror optics for imaging two cube faces

A single camera can inspect two adjacent faces of a cube in one exposure. A first-surface mirror at 45°, mounted beside the part, folds the side face into the same lens that views the face directly, and both views land side by side on one sensor. One camera, one trigger, one calibration — the same fold covers round parts, pills and moving webs in production use. This page gives the geometry rules, a worked sizing example with the arithmetic shown, the alignment checks that make the fold hold, and the cases where a second camera remains the better answer.

What a folded two-face view looks like

Point the camera down at the part. The top face is imaged directly onto one half of the sensor. A first-surface mirror standing beside the part, tilted 45°, catches light from an adjacent side face and folds it upward into the same lens. One frame then holds both views, ready for one monitor and one inspection routine.

The fold costs three things, and each drives the design:

1. Half the sensor per view, so magnification is half of a single-face design.
2. A mirrored, rotated image: one reflection reverses handedness, so the folded half arrives rotated 90° and flipped. Calibration absorbs the geometry; readable text needs a software flip.
3. One shared depth of field: both faces must be sharp in the same exposure.

Software treats each half as its own inspection region, the same discipline as two locates instead of one generic pick in robot guidance. The trick is proven well beyond cubes: the same fold images fruit surfaces, pharmaceutical pills and, with line scan cameras, several sides of a moving web.

Why the mirror must be first-surface

An ordinary glass mirror reflects twice: about 4% of the light bounces off the front surface, and the rest reaches the coating through the glass. The result is the real image plus a fainter ghost, displaced by roughly twice the glass thickness — more at a 45° fold. With 3 mm glass the ghost lands several millimetres away in object space, which at 0.10x is on the order of a hundred sensor pixels: wide enough to corrupt any measurement it touches.

A first-surface coating moves the reflection to the front of the glass. One reflection, no ghost. The coating is soft and damages easily, so mount it coated-side toward the part and clean it the way you would clean a front element, as described in how to clean a machine vision camera window safely.

Expect roughly 90% reflectance from a typical metallic coating: the folded half is about 0.15 stops dimmer than the direct half. Match it with exposure, or with a slightly stronger light on that leg.

The geometry: equal legs, a true 45°, a big enough mirror

Four rules size the fold:

Equal optical path. Both faces are sharp in one exposure only if lens-to-mirror plus mirror-to-face equals the direct working distance. Hold the sum inside the depth of field.

A true 45°. A flat mirror doubles angular errors: 1° of tilt rotates the folded view by 2°. True the mirror to about ±0.5° against a square target before calibrating.

A mirror at least as long as the field. The coating must intercept the whole folded field, so the mirror edge should exceed the face coverage — a 44 mm field wants a 50 mm square mirror.

Room beside the part. The folded leg needs clear space roughly as long as the direct leg. If the total comes out shorter than the lens minimum, extension tubes for close-up machine vision bring focus back in.

Worked example: two 44 mm views of a 40 mm cube at 0.10x

Inputs: 40 mm faces with a 10% margin, so 44 mm of coverage per view; a 2/3" camera with an 8.8 × 6.6 mm active area, 2560 × 1920 pixels of 3.45 µm (illustrative values for a typical 2/3" sensor); the two views stacked along the 8.8 mm width; a 35 mm lens from the machine vision lenses range.

Magnification: each half of the sensor is 4.4 mm wide, so m = 4.4 mm / 44 mm = 0.10x.

Working distance: WD = 35 mm × (1 + 0.10) / 0.10 = 385 mm to the direct face.

Field check: 8.8 mm / 0.10 = 88 mm of total field, and two 44 mm regions fill it exactly, with no gap. Cutting the margin to 5% gives 42 mm per face, m = 4.4 / 42 = 0.105x, WD ≈ 369 mm and a 4 mm dark strip between the views — usually worth having.

Pixel size: 3.45 µm / 0.10 = 34.5 µm per pixel in object space. The 44 mm region spans 4400 µm / 34.5 µm ≈ 1280 pixels — the full half-sensor — and the 40 mm face itself spans about 1160 pixels.

Fold legs: 300 mm lens-to-mirror plus 85 mm mirror-to-face = 385 mm, matching the direct path.

Depth of field: at F4 with a 2-pixel circle, c = 6.9 µm, DOF ≈ 2 × 4 × 0.0069 mm × 1.10 / 0.01 = 6.1 mm total, about ±3 mm. Legs held to ±3 mm stay in focus. At F5.6 the DOF grows to ≈ 8.5 mm but costs one stop of exposure.

Exposure: the part is static on the stand, so there is no motion limit; start at 10 ms under a bright LED bar at F4 and trim by histogram. On a belt at 50 mm/s the blur budget is 0.5 px = 17 µm, so t ≤ 17 µm / 50 mm/s = 0.34 ms — strobe. At the 10 ms static exposure, the same budget allows only 17 µm / 10 ms = 1.7 mm/s of motion.

The decisions: 35 mm at 0.10x, 385 mm working distance, 300 + 85 mm legs, F4, and a first-surface mirror of at least 50 mm square. Strobe at 0.34 ms or shorter once the part moves.

Cross-check other focal lengths for the same field with the focal-length calculator:

The lens that hits these numbers is the LS-FFL-0679, a 35 mm, 2/3", 6 MP, C-mount machine vision lens.

Mirror, prism or a second camera

For a telecentric direct path, a prism behind the lens folds the cone without disturbing magnification. The LS-LXR-0144 is a double-fold prism for telecentric lenses that turns the output 90° over a 30 mm optical path.

A fixed-magnification path of this kind is the LS-TCL-0574, a 0.4x fixed-magnification lens with a 227 mm working distance, C-mount, for a 1.2" sensor. Whether that trade fits the part is the subject of entocentric vs telecentric lenses.

Mounting and calibration

Rigidity decides whether the fold survives a bump, so put the camera on a tall, stiff column from the camera stands category rather than a lab clamp. One slide-table stand that suits this geometry is the LS-MNT-0040, a professional camera stand with a 700 mm column height and a 400 × 450 mm base.

That column clears a 385 mm working distance with room for the mirror and its bracket above the stage. True the mirror angle to ±0.5° by comparing the folded view with the direct view of a square target. A manual XY and rotation stage makes the adjustment repeatable.

Calibrate once, after the mirror is fixed, with a target that shows corners through both halves; the single intrinsic set then covers both regions. Hold residuals to the levels in camera calibration residual values: average and max targets, and keep the target inside the covered area using the margins in calibration target field of view and lens coverage margins.

Light both legs. The folded face is the one that ends up in shadow, so give it its own LED aimed past the mirror, or sequence the two lights as in sequential machine vision lighting for multi-view inspection. The wider stability order — light first, then lens, then exposure — is laid out in stable 2D vision inspection systems.

Where one camera falls short

• Glossy faces. Polished or plated faces mirror the scene, including each other and the fold mirror itself. Cross-polarization — two polarizers crossed at 90° — removes that sheen; the method is in cross polarization machine vision: reduce surface glare.
• Different exposures per view. A dark top face and a bright side face want different shutter times, but one sensor gives one exposure per frame. Alternate two exposure times across consecutive triggers if the part presents itself twice — see two exposure times, one camera.
• Depth. The fold adds no height data. Tilt, volume or 3D position is a different system choice; start from 2D or 3D camera for conveyor pick and place.
• Fixed geometry. The fold is sized to one face size and one working distance. A part family spanning, say, 30-60 mm faces breaks the equal-leg rule; refixture per size or move to two cameras.
• Fixture access. The folded leg needs a clear line to the side face. A clamped or enclosed side cannot be the folded view.

Before you order

Sizing

• Fix the face size and the margin, 5-10%. This sets magnification, working distance, pixel size and mirror size; everything else follows from it.
• Check for clear space beside the part for a folded leg about as long as the direct one.

Hardware

• First-surface mirror, coated side toward the part, edge at least the face coverage — 50 mm square in the example.
• Mirror trued to ±0.5°, legs equal within the depth of field (±3 mm at F4 in the example).
• Stand and bracket stiff enough that a bump cannot move the fold.

Set-up and run

• One calibration after installation, with a target visible through both halves.
• Light for both legs, with histogram peaks below saturation on both.
• Software rotates, and where needed flips, the folded half before matching.
• Re-check leg equality and angle after any collision or rebuild.

Sized this way, the fold behaves like a second camera that shares the first one's calibration and trigger. Pick the direct-path lens in the lens finder, the fold hardware from the lens accessories category, and feed your own face size and margin into the system configurator. Builds in the same family sit on the systems topic page.